NUMERICAL RESOLUTION OF THE BOUNDARY INTEGRAL-EQUATIONS FOR ELASTIC-SCATTERING BY A PLANE CRACK

The problem of wave scattering by a plane crack is solved, either in t he case of acoustic waves or in the case of elastic waves incidence us ing the boundary integral equation method. A collocation method is oft en used to solve that equation, but here we will use a variational met hod, first writing the problem of Fourier variables, and then writing the associated integrals in the sesquilinear form with weak singularit y kernels. This representation is used in the numerical approach, made with a finite element method in the surface of the crack. Numerical t ests were made with circular and elliptical cracks, but this method ca n be extended to other shapes, with the same convergence profiles. Ext ensive results are given concerning the crack opening displacement, th e scattering cross-section, the back-scattered amplitude and far-field patterns.